17.1 Quick: complete pooling option

\[Y_{ij} | \beta_0, \beta_1, \sigma \sim N(\mu_i, \sigma^2)\] \(Y_{ij}\) running time with \(j\) runner and \(i\) race

\[\mu_i = \beta_0 + \beta_1X_{ij}\] \(X_{ij}\) Age

Then we have global parameters (also here priors)

\[\beta_{0c} \sim N (0, 35^2)\] This is the intercept centered

\[\beta_1 \sim N(0, 15^2)\]

\[\sigma \sim Exp(0,072)\]

If we go with this model: no relationship between age and running time.

complete_pooled_model <- stan_glm(
  net ~ age, 
  data = running, family = gaussian, 
  prior_intercept = normal(0, 2.5, autoscale = TRUE),
  prior = normal(0, 2.5, autoscale = TRUE), 
  prior_aux = exponential(1, autoscale = TRUE),
  chains = 4, iter = 5000*2, seed = 84735)

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